Question

a regular pentagon is rotated about its center. what degree of rotation maps the pentagon onto itself?

Explanation:

Step1: Find full rotation angle

A full rotation is $360^\circ$.

Step2: Divide by number of sides

A regular pentagon has 5 equal sides/angles. Calculate $\frac{360^\circ}{5}$
$\frac{360^\circ}{5} = 72^\circ$

Answer:

$72^\circ$ (and multiples of $72^\circ$, such as $144^\circ$, $216^\circ$, $288^\circ$, $360^\circ$)